A beam of protons is injected into the velocity selector. The magnetic field is

Question

A beam of protons is injected into the velocity selector. The magnetic field is 20 mT directed out of the page. A. If the protons are to have a speed of .6 c (c = speed of light), find the size & direction of the magnetic force acting on the protons. B. What magnitude of the electric field is required to select protons at .6 c? Is the top plate positively or negatively charged? Explain C. If the beam is replaced with a beam of electrons traveling at the same speed, do the electrons pass through velocity selector undeflected, strike the upper plate, or strike the lower plate? Explain Velocity Selector Magnetic Field,B, is out of the page

Explanation / Answer

Part A)

The magnitude of the magnetic force is determined by the expression

F = q v x B bold letters indicate vectors

F = q v B Sin

F = 1.6 10-19 0.6 3 108 20 10-3 Sin 90

the magnetic field is out of the page and the velocity is parallel to the page, so there are 90 degree between the two

F = 5.76 10-13 N

The direction of the force is given by the right-hand rule, the thumb points to speed, the other fingers of the countryside and the palm force, so the strength goes down

Part B)

To have a gear selector forces must be equal

FE = FB

FE = q E

E = FB /q

E = 5.76 10-13 / 1.6 10-19

E = 3.6 106 N/C

As the magnetic force going down the electric force should go up so the upper silver should be negatively charged

Part C)

Electrons are negatively charged so the direction of the magnetic force changes direction accordingly must change the direction of this electric field to the top plate must be negative

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